ALBANY — Gov. Eliot Spitzer may propose a ceiling on annual property tax increases, an idea he has rejected before and one that has often met resistance among fellow Democrats.

The proposal’s backers see it as a way of containing the property tax burden on Long Island and in upstate communities. It is among the ideas the governor is considering announcing in his annual address to the Legislature on Wednesday. In particular, he is thinking of setting up a commission to study how best to structure a tax cap — a number of alternatives have been sketched out in the past.

The proposal, reported by The New York Sun on Monday, is still being debated within the administration and is not certain to appear at all in the speech, according to a person who has been briefed on the deliberations.

Much of the speech is still in draft form, and some of the ideas that have been mentioned may not be included in the final address.

One of the more certain proposals is selling a stake in the state lottery in hopes of raising billions of dollars for a new endowment for the state’s higher education system, said two people who have been briefed on the plan.

As envisioned, that plan would not fully privatize the lottery system, and the state would retain control. The governor is hoping to raise $4 billion for the endowment, which would provide annual operating aid for the State University of New York and the City University of New York. The governor has made shoring up the state’s higher education system a top priority. The administration seems likely to try to hire an investment bank to plan how to raise the money.

In a year when money is tight, other steps being considered are more cosmetic. For example, the governor plans to propose renaming the Triborough Bridge after Robert F. Kennedy.

Most of the proposals in the speech would require the approval of the Legislature, which has had a contentious relationship with the governor.

Mr. Spitzer’s speech will be the first major address of his second year in office and will give him a chance to turn around his embattled governorship. He faces three continuing investigations into efforts by his administration to discredit his main political rival, the Republican Senate majority leader, Joseph L. Bruno.

After unsuccessfully tacking left on a number of issues — most notably his abandoned plan to allow illegal immigrants to apply for driver’s licenses — a ceiling on property tax increases would be something of a move in the other direction. The proposal is likely to be opposed by teachers’ unions, but such caps have been embraced in states including Massachusetts and just last year in New Jersey.

“It is practical, because it has no direct, immediate budget impact,” said Edmund J. McMahon, director of the Empire Center for Public Policy, a conservative group, and a longtime advocate of a cap. “It’s proven because it’s worked in Massachusetts, and it’s simple,” he added.

But Richard C. Iannuzzi, president of New York State United Teachers, said, “It puts an artificial cap on the ability of local communities to provide the public services that they believe they should provide.”

“You’re putting a ceiling on poor districts that they will almost never get the support to overcome,” he added. “It creates a greater divide between rich and poor.”

There are a number of ways to structure caps on the property tax, although often they restrict tax increases to around 4 percent, with some exceptions and with the provision that voters can override them.

New York’s property tax burden is among the highest in the nation, but is felt most acutely outside New York City, where the city income tax helps finance schools. Over the years, a system of rebate checks and other state aid aimed at homeowners, known as the School Tax Relief program, has only appeared to give localities the license to spend more, critics have said, because it is not accompanied by a cap.

Scott Reif, a spokesman for Senate Republicans, said that he had not seen a property tax proposal and that the Republicans had no such proposal on the table themselves, but “we have supported legislation in the past that would give voters the authority to enact a property tax cap at the local level.”

Dan Weiller, a spokesman for Assembly Speaker Sheldon Silver, a Democrat, said, “We haven’t seen the proposal, so we can’t comment.”

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